This section contains a very comprehensive description of the solution to Igo Hatsuyōron 120. The choice of the order of moves in it pursues the purpose of offering the reader an approach to the particular elements of this problem, as well as to the historical process of its decoding, that is as easy to grasp as possible.

The interested reader will find branches to all other, much more detailed, sections of this New Story Line 2022 as well as references to the older parts of our intensive analysis.

Igo Hatsuyōron 120 was first published in 1982 in a book written by Fujisawa Hideyuki 9p after an old edition of the problem collection was discovered by Araki Naomi, which apparently contained only the problems of the original version, including two previously unknown, one of which was Inoue Dōsetsu Inseki's masterpiece.

At that time, Inoue Dōsetsu Inseki's problem collection itself had already been known to the general public for more than a century.

In his postface, Inoue Dōsetsu Inseki insists on the necessity, for the study of these problems to bear fruit, to give no indication about them (except whose turn it is), not even the objective to reach.

Let's enter the world of amateurs, arriving about two decades later ...

Once upon a time, Joachim Meinhardt counted the stones on the board and found to his surprise that White has a surplus of one stone, as there are 70 Black stones, but 71 White stones. Please remember that it is Black to move.

Our long-standing assumption was that White captured a Black stone that was positioned at , and connected at this point later.

However, recent findings, obtained with the support of KataGo, have shown us that White had not in fact captured an additional Black stone before the problem began, but had started the game.

For further details, please refer to section "Black's Missing 71st Stone – Vanished" ( 2023).

Let's now enter the analysis room for a detailed explanation of a rewrite of Our Solution to the problem ...

Please note that we still worked with our original assumption in this 2022 Story Line, for better comparability with our earlier analyses. This implies a komi of one point for White.

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Action starts in the lower right corner with Black's solid connection at .

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White prevents her stones at the right edge from being easily and quickly captured.

After Black's initial move, there are a variety of options for changing the order of moves during the sequence in the lower right corner.
We will follow the classical line here for a while.

:
Black does the same for his two stones to the right.

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White tries to escape.

:
Black has to make sure that White's stones do not break through to their waiting allies in the centre.

KataGo likes to start the reduction of White's upper right corner "very early", so interrupting the process of creating a hanezeki in the lower right corner.
This reduction starts with the push at , which has also been played by Fujisawa Hideyuki, but much later in the course of his solution sequence.

Harry Fearnley discovered that the hasami-tsuke at – a typical endgame move – is a better follow-up move for Black than the push at that has been used by Fujisawa Hideyuki.

Harry's Hasami-Tsuke would make no difference in the classical solution, but would give Black a noticeable benefit after my later Guzumi .

For further details, please refer to section "Harry's Hasami-Tsuke Sequence" ( 2024).

This is also the first and, for a long time, the only moment when KataGo seriously considers my Guzumi.
It would result a "simple" change in the order of moves.

For further details, please refer to section "The Earliest Possible Moment for Playing my Guzumi" ( 2028).

:
White continues her attempts to escape.

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Black, on the other hand, tries his best at fencing in.

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White must not cut at the other side with , as Black's bottom group would subsequently get enough liberties to kill the White corner.

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White's (and Black's) forces are now cut in two.

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Black starts spoiling White's shape by creating several cutting points.

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White must secure the connection of her stones.

The result is a (temporary) seki in the middle of the right side.

Before starting the creation of the real hanezeki in the lower right corner, Fujisawa Hideyuki inserted the kikashi of , and , in the (temporary) seki / .

For further details about the first throw-in , please refer to section "Fujisawa Hideyuki's First Throw-in" ( 2025).

Cheng Xiaoliu 6p described an improvement for Black in his 1988 book, a third kikashi , , which had to be played immediately afterwards.

For further details, please refer to section "Kikashi in the Hanezeki" ( 2027).

I found another – decisive – improvement for Black, the Second Throw-in with . White is forced to capture with , whereafter Fujisawa Hideyuki's moves , follow.
After this improvement, it was no longer necessary to play Cheng's kikashi of , "early" in the game.

For further details about the second throw-in at , please refer to section "My Second Throw-in" ( 2026).

First and second throw-in contain an outright loss of two points for Black (the two captured stones and ) in those cases where the forthcoming hanezeki is not resolved. However, this specific disadvantage allowed for an alternative solution.
Since the existence of two equivalent solutions contradicts the classical principles of tsume-go, the "early" kikashi in the (temporary) seki must inevitably be dispensed with.

As a matter of course, even with "early" played throw-in in the hanezeki, Black would not be forced to also play my Guzumi "early".

Typically for an AI programme, KataGo plays the entire sequence of all available kikashi (, , , , , , , , , ) "early".

In order to simplify the following commentaries, we will shade out the region of the (temporary) seki as long as necessary. Please consider it played out according to the context.

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Black's atari starts the creation of the hanezeki in the lower right corner.

The further course of its process is a strict one-way street.
Please refer to the history of our research for "simple" straightforward refutations of imaginable alternative options whose explicit treatment you may miss here. ...

39

Please be aware that Black can neither break through to his allies in the left centre with his large group in the upper right, nor kill White's lower edge. Therefore, simply living in the lower right corner is no valid option for Black.

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White's kikashi in the corner ...

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... leads to the creation of the Black three-stone group inside the hanezeki.

Black must not let live White independently in the corner (by mistakenly capturing at ), as his large group in the upper right still lacks a second eye.

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White establishes her own three-stone group in the hanezeki.

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Black starts the creation of the hanezeki's tail.

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The hanezeki's tail has reached its minimum length of two stones.

A simple "hane" (i.e. doing without ) would not be sufficient here.
If Black played elsewhere, a White move at would be sente, forcing Black to occupy one of the two shared liberties in the hanezeki.

The hanezeki in Igo Hatsuyōron 120 is a very special one; not only because of its two shared liberties at the lower edge, but also due to its interconnection with the temporary seki in the middle of the right side (shaded here).
This results in some special features without which this problem would not really work.

For further details, please refer to section "Igo Hatsuyōron 120's Hanezeki" ( 2044).

:
KataGo likes to start the reduction of White's upper right corner immediately or soon after the creation of the hanezeki has been completed, i.e. after the hanezeki's tail has reached its minimum length of two stones.

For further details about the ensuing corner reduction, please refer to section "Harry's Hasami-Tsuke Sequence" ( 2024).

In his 2010 book, Cheng immediately continued the tail's walk across the board with a move at .
In the classical solutions, the reduction of Black's upper right corner is played after the creation of the nakade at the left edge, just because it ends in gote.

This is the second moment when KataGo seriously considers playing my Guzumi (please remember that KataGo had already played both throw-in and kikashi in the hanezeki at this moment in the game).
However – contrary to the push into White's corner – playing my Guzumi so early would be a grave mistake, losing one point overall.
Black must wait at least until the hanezeki's tail has reached a length of four stones.

For further details, please refer to chapter "Timing of the Guzumi (2022)" ( 1814) and ...

... to chapter "Timing of the Guzumi Before Harry's Hasami-Tsuke Sequence (2022)" ( 1864).

Please note that we have refrained from using an "early" Guzumi in the main line of this elaboration in order to achieve a better match with the historical conditions.

: (30 2022a)
White blocks immediately.

In principle, White could also retreat with , not affecting the outcome of the game.

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This hasami-tsuke has been found by Harry Fearnley.

Harry's Hasami-Tsuke is a genuine endgame move, but does not have any effect in the classical solutions. Due to the relationship of liberties in the forthcoming Main Semeai, Black will have to sacrifice his hasami-tsuke stone in these lines, so that White will get as much territory in the corner as after the classical reduction sequence , , by Fujisawa Hideyuki (played after the forthcoming creation of the nakade at the left edge, as this ends in gote).

For further details, please refer to section "Harry's Hasami-Tsuke Sequence" ( 2024).

:
Black starts the journey of the hanzeki's tail through the centre of the board, during which potential White territory in this area will be wiped out.

Please remember that White must not let the hanezeki's tail get two outside liberties, as Black could successfully resolve the hanezeki under this condition.

:
For the next few moves White will have to prevent stones of hers from being cut off and captured.

This further course the hanezeki's tail through the centre of the board is a one-way street again.
Please refer to the history of our research for "simple" straightforward refutations of imaginable alternative options whose explicit treatment you may miss here ...
39

:
Black continues with walking the hanzeki's tail.

Please note that Black will have to sacrifice , in order to remain par with the Punishment Semeai Level, as long as my Guzumi has not been played.

As an alternative option, KataGo also considers playing my Guzumi at .
After doing so, KataGo will not choose the "usual" line of play by completing the Guzumi Exchange with , but enhance her position at the bottom with a move at .
The subsequent sequence of moves will resemble a "real" game much more than the known solution to the problem. However, nothing will change in the result of the game!

This "real" game sequence that is shown in the subvariation is the (seemingly) equivalent solution mentioned above, which existence would contradict the classical principles of tsume-go that require only one single valid solution (changes in the order of moves are not considered).
In this variation, the hanezeki remains stable, so losing two points through inserting the kikashi in the hanezeki "early" was a grave mistake by Black.

Please remember that KataGo played all kikashi in the (temporary) seki in the middle of the right side much earlier.

For further details, please refer to section "The Earliest Possible Moment for Playing my Guzumi" ( 2028) ...

Please note that we have refrained from using an "early" Guzumi in this elaboration in order to achieve a better match with the historical conditions.

:
Black's peep at the second line serves strengthening his position in the lower left corner.

This move could be played even later.

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From here on, White is unable to stop the tail's walk, e.g. with (a geta at would leave the tail with two outside liberties from the very outset), because connecting the tail to the outside or reducing White's then cut-off bottom group to only one eye are (forcing White to capture the hanezeki's tail for survival) miai for Black.

:
Playing at or at , instead, would allow the hanezeki's tail to get two outside liberties, enabling Black to successfully dissolve the hanezeki after connecting at .

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Black pushes upwards.

Playing the wedge at , instead, would result in his large group in the upper right losing a decisive Main Semeai Liberty, and therefore is out of the question, in principle.

Joachim investigated this alternative move (at a time when both throw-in in the hanezeki were played by us), having a semeai with White's centre group in mind.
However, as it turned out, Black will not be successful.

For further details, please refer to section "Black's Wedge in the Centre (Joachim's Ko-Semeai #3)" ( 2029).

:
Black pushes upwards.

Typical for AI, KataGo likes to change the order of moves here, and give atari with first.
It results a change in the order of moves with , , .

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White connects her stone in atari.

She is unable to successfully fight the ko that would develop in the centre after , , , .
Black will be able to capture White's corner group, so winning the game.

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Black pushes to the left.

Joachim investigated Black's hane at as an alternative move (at a time when both throw-in in the hanezeki were played by us), having a semeai with White's centre group in mind.

Joachim's investigation resulted in an intense ko fight, but which White will win by one move.
However, in its first training session of 2019, KataGo was for a long time so convinced of a Black success in Joachim's Ko-Semeai that it tried to develop alternative ways of play in the very beginnnig instead of forming the hanezeki.
But in the end, KataGo also found the decisive move for White, which Joachim had also been searching for for a long time.

For further details, please refer to section "Black's Hane at the Top (Joachim's Ko-Semeai #2)" 2030)

:
White has to block from above.

Playing at from the left would result in another ko-fight at the top (similar to that a few moves earlier) after the sequence of , , , , , which White will lose.
In his 2010 book, Cheng chose to show this alternative ko-fight at the top, instead of the one in the centre.

Please note that White has not had an opportunity so far to tenuki for playing in the (temporary) seki first.

:
This effect seems counterintuitive, but Black's first throw-in in the hanezeki will benefit Black by one point in the Capture Variation.

In the classical line of play (based on Fujisawa Hideyuki's solution), however, Black's first throw-in is mandatory in order to reduce the liberties of White's group in the temporary seki.

Assuming the further kikashi of , , , , two liberties will remain that are shared between Black's and White's group in the temporary seki.

However, if White ever got the opportunity to connect at (so losing one tempo in the forthcoming Main Semeai), there would be four shared liberties (after the exchange of , ), i.e. a net gain of one liberty.
Thus, with neither Harry's Hasami-Tsuke nor my Guzumi already played, Black would fall prey to the Punishment Semeai.
Please note that with Fujisawa Hideyuki's type of corner reduction, Black does not have any option to exchange points for Main Semeai Liberties.

For further details, please refer to section "Fujisawa Hideyuki's First Throw-in" 2026)

The series of kikashi in the hanezeki could basically be delayed until before the last Black move to complete the forthcoming nine-point nakade at the left edge.

We follow the historical development here, where we played the two remaining kikashi in the hanezeki (both throw-in were played before the creation of the real hanezeki) just now.

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Black's group in the (temporary) seki lost one liberty by White's move at . Therefore, it is mandatory to play my Second Throw-in at just now.

Otherwise, White would connect at at the earliest possible moment (e.g. would not be absolute sente in this case), so threatening to capture Black's stones below. Black would have to play at , occupying one of White's outside liberties.
That would be a change in the order of moves with Fujisawa Hideyuki's immediate kikashi from the outside explained below, which costs Black one point overall.

Fujisawa Hideyuki continued immediately with (much earlier in the game, of course), forcing White to answer with . He commented that it would not be good to take Black's large group a liberty (what is done by in the following diagram).

However, he seems to have overlooked the fact that the number of internal liberties inside the hanezeki, which are shared between Black's large group in the upper right and White's upper group in the temporary seki, is irrelevant for a semeai between groups outside the hanezeki, as long as Black's large group does not gain a potential approach-move liberty, as is the case with Fujisawa Hideyuki's way of reducing the upper right corner.

For further details, please refer to section "My Second Throw-in" 2026)

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Black is forced to solidly connect his partial groups in the upper right – sooner or later.
And he must do so in sente. Please note that he threatens to give atari with after this connection.

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White is forced to fill one of her false eyes, erasing her current damezumari, and also completing the seki in the middle of the ride side.

This additional seki serves as a buffer between Black's large group in the upper right and the true hanezeki that will emerge in the lower right corner.
This buffer achieves two goals:
– Firstly, it lengthens the forthcoming Main Semeai slightly, but decisively.
– Secondly, the results of the two Main Variations of the dissolving of the hanezeki are largely aligned.

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Black's upper kikashi in the hanezeki is an invention of Cheng, introduced in his 1988 book.

It was mandatory in the classical solution, in which my Second Throw-in was not played ( would be empty then), to insert this kikashi as early as possible.
Otherwise, White would play and in sente (threatening to capture Black's group in the hanezeki below), so Black would have to answer with and , providing White with an additional profit of two points (one point of territory and one prisoner at ) in the Semeai Variation, in which Black's large group in the upper right becomes captured.

For further details, please refer to section "Kikashi in the Hanezeki" ( 2027).

This is the position in which Michael Redmond had recommended his Kikashi in the Bamboo Joint, as a follow-up move to Harry's Hasami-Tsuke Sequence that at that time had been played by us just before the start of the Crosscut Sequence in the left centre.

For further details, please refer to section "Michael Redmond's Kikashi in the Bamboo Joint" ( 2032).

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White is forced to connect.

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Black's second kikashi in the hanezeki.

We played the two kikashi in the hanezeki in reversed order, but which does not matter.

:
Now let's return to the main event on the board.

Black pushes to the left for another time, initiating the Crosscut Sequence in the left centre.

For a long time, we thought that this was the latest moment to play my Guzumi .
As we now know, the Guzumi could be played even some moves later.

For further details, please refer to section "My Guzumi" ( 2031).

The 2019 version of KataGo played my Guzumi also just now, before the start of the Crosscut Sequence in the left centre.

The 2021 version of KataGo usually plays the Guzumi Exchange , earlier in the game.

For further details, please refer to chapter "Timing of the Guzumi (2022)" ( 1813).

:
White connects her stone in atari.

Fujisawa Hideyuki shows a subvariation in which White captures the hanezeki's tail with , instead. His sequence contains the oki at as third move.
But as a matter of course, conditioned by the specific nature of this particular Hanezeki, this oki does not help White winning the ensuing semeai in the lower right corner.
This may have been the reason why he did not use this oki later in the Capture Variation of the Main Semeai, not being aware of its territorial importance.

For further details, please refer to the history of our research ...
519

Please note that this subvariation contains my Second Throw-in, but which will not affect its outcome.

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Black saves his just played cutting stone.

Fujisawa Hideyuki comments that Black must not connect the hanezeki's tail, instead.

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White secures independent life for her cut-off bottom group.

Fujisawa Hideyuki also shows that White is unable to play at , instead.
Black would reduce White's bottom group to only one eye with , and win the semeai with his large group in the upper right by one move.

For further details, please refer to the history of our research ...
725

:
Black solidifies the border of his upper left corner by connecting his second cutting stone with .

Joachim examined two conceivable alternatives very intensively:

Playing the hiki of prevents Black's single stone at the upper edge from becoming captured, and will result in a fierce semeai between Black's large group in the upper right and White's group at the top / in the centre.

For further details, please refer to section "Joachim's Hiki at the Upper Edge (Joachim's Ko-Semeai #1)" ( 2034) ...

Black is able to capture most of White's stones at the left with a move at . However, he will not be successful overall, as he has left his top left corner with massive (and quite surprising) weaknesses.

For further details, please refer to section "Joachim's Capture of White's Left Side" ( 2035).

Joachim's investigations into these Black alternative moves took place at a time when the two kikashi in the hanezeki (, ) had not yet been played by us so early. Both kikashi could perhaps become important as Black ko-threats (especially with Joachim's Ko-Semeai).

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White's group at the left side of the board is now separated from the rest of the board.
White must attack Black's five-stone group at the left edge, in order to stop Black from capturing her stones quite easily.

This move triggers the ensuing Nakade Sequence.

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Black cuts White's forces apart, in order to minimise the eye space of her left-hand group.

The creation of Black's nakade at the left edge of the board is a one-way street, in principle.

For further details, please refer to the history of our investigations ...
503

Quite surprisingly, in this position without the Guzumi Exchange , played beforehand, Black must not change the order of moves and push at , instead.
Black would lose one point overall unnecessarily.

For further details, please refer to chapter "Timing of the Guzumi (2022)" ( 1822).

Please note that Fujisawa Hideyuki (and also Cheng) – apparently not being aware of Harry's Hasami-Tsuke and my Guzumi – mistakenly started the fight at the left edge with the push to .

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This is the truly verly last moment to initiate the Guzumi Exchange in the upper right, according to KataGo, starting with my Guzumi in the upper right.

For further details about the timing of this move, please refer to chapter "Timing of the Guzumi (2022)" ( 1813).

My Guzumi provides Black's large group in the upper right with an additional approach-move liberty, enabling Black to survive the Punishment Semeai even after connecting the hasami-tsuke stone .
Consequently, we will finish the additional marking of the hasami-tsuke stone here.

For further details, please refer to section "My Guzumi" ( 2031).

:
White's answer is forced.

The 2019 version of KataGo also considered the solid connection at (and often played it in self-play games), which will not affect the Main Semeai.
However, this alternative could be evaluated as a technical mistake, as it leaves a Black ko-threat with .

After the first analyses of my Guzumi, we played it immediately before the start of the Crosscut Sequence in the left centre, which opened up the principle possibility of a tenuki for White, in particular to attack Black's upper left corner.
However, no move other than leads to success.

For further details about these earlier tenuki options, please refer to chapter "Tenuki Variations Before the Crosscut Sequence (2022)" ( 1432).

:
Black continues to reduce White's group to only one eye.

:
KataGo unearthed this surprising atari within the Nakade Sequence.
KataGo's Atari can only be played at one single moment in time, and that is right now.

For further details, please refer to the history of our investigations ...
1093a

We also had this atari in focus once a very long time ago, but today we have to admit that we were not persistent and consistent enough in our analysis at that time.
We had tried it both after completing the nine-stone nakade and at several earlier times in the Nakade Sequence when the atari is not successful. Due to the lack of success, we had then stopped our analysis, shortly before reaching the goal of the working moment, as it seems today.

For further details, please refer to section "KataGo's Atari in the Nakade Sequence" ( 2036).

In the pre-AI era, this move had been played at , giving atari at Black's group to the left immediately.

: (97 2022b)
Black strengthens his shape in the left centre, in sente.
This straightforward defense was favoured by KataGo's 2019 version.

KataGo's 2021 version favours playing at immediately, which is an equivalent option.

:
White's connection is forced, also being an atari at Black's eight stones to the left.

:
Black creates a nine-stone lump whose capture will result in only one eye for White.

:
Now, White is able to capture Black's single stone below the nakade, achieving a quite large benefit.

:
Black's connection, solidly defending his lower left corner, is forced.
Please note the cutting point in the lower left centre that Black will now have to worry about.

If Black mistakenly played tenuki, White would first capture Black's nakade with , in order to erase the shortage of liberties of her three stones in the lower left corner.
If Black insisted on keeping White's group down at only one eye at the left edge, White would continue with , , , and Black would be unable to save his three stones, due to , , , .

Giving atari with , instead, was suggested by Harry, but Black cannot hope on winning an ensuing ko. Most likely, a change in the order of moves will result, as Black would have to connect at – sooner or later.

:
This tsuke was shown to us by Yamada Shinji 6p at a time, when the endgame at the left side of the board had been started after the dissolving of the hanezeki.

For further details, please refer to section "Yamada Shinji's Tsuke" ( 2037).

It was Prof. Jeong SooHyun 9p from Myongji University in Seoul, who pointed out to us that the endgame on the left side of the board had to be started "early", as the Main Semeai as such had already been decided.

For further details, please refer to section "Prof. Jeong SooHyun's Advice to Start the Endgame Early" ( 2043).

The classical line of play (as a matter of course without my Second Throw-in, Harry's Hasami-Tsuke and my Guzumi) continued with the mutual occupation of opponent's liberties in the Main Semeai, and started the endgame with the atari of in the upper left corner after the dissolving of the hanezeki.

Please note that Fujisawa Hideyuki only gave the first two moves of the endgame in his 1982 book (, ), but refrained from showing the subsequent sequence.

: (A 2022c)
Black's block is the only move here.

Black is unable to confine White's intruder successfully in the corner by playing at , instead.

:
KataGo plays the crosscut of immediately after Black's block. This move gains one point on its own.

However, it must be played quite early, in any case before Black consolidated his corner by occupying both points .

This implies that KataGo's Immediate Crosscut was not possible in the era of Yamada Shinji.
Yamada Shinji continued with drawing back to , instead.

For further details, please refer to section "KataGo's Immediate Crosscut after Yamada Shinji's Tsuke" ( 2038) ...

... and to section "Yamada Shinji's Tsuke" ( 2037).

:
Black has to give atari from the inside.

As before, playing at , instead, will not lead to success.

For further details, please refer to section "KataGo's Immediate Crosscut after Yamada Shinji's Tsuke" ( 2038).

:
White has the opportunity to give atari at the upper edge, before ...

:
... drawing back to , saving her pivotal tsuke stone.

:
It is best for Black to defend his territory in the upper left corner by giving atari at White's single stone at the upper edge.

Blocking the lower left corner with , instead, is possible, not affecting the overall result of the game here.
However, the Semeai Variation will become a few points worse for Black.

For further details, please refer to section "KataGo's Immediate Crosscut after Yamada Shinji's Tsuke" ( 2038b).

Please note that this descent to the lower edge may well be the means of choice in other circumstances.

:
White continues the endgame with a hasami-tsuke in the lower left corner.

The endgame on the left side of the board in the "classical" environment (i.e. with Fujisawa Hideyuki's Atari instead of Yamada Shinji's Tsuke) has been (also) developed by Jérôme Hubert.

For further details, please refer to section "Jérôme Hubert's Correction of the Mutual Occupation of Opponent's Liberties" ( 2041).

Cheng shows another suggestion for this endgame explicitely in his 1988 book (which is the same as Jérôme Hubert's in the beginning, but will deviate later).

For further details, please refer to section "Jérôme Hubert's Correction of the Mutual Occupation of Opponent's Liberties" ( 2041).

:
Black's answer is forced.

:
KataGo likes to insert this kikashi "early".

:
This tenuki to the upper left corner is an invention that Cheng described in his 1988 book.

It favours Black over the solid connection at used by Jérôme Hubert.

:
White captures one Black stone in the lower left corner.

:
Black is forced to connect.

:
It follows another "early" kikashi in the upper left corner, again typical for KataGo.

:
This bad-shape move in the left centre is the third of KataGo's findings. In principle, it is gote locally, also losing one tempo in the Main Semeai.

However, after decidedly intensive analysis, it will turn out that – due to his weakness of the cutting point – Black will have to make a protective move in the left centre before occupying White's liberty at , which will give White the just lost Main Semeai Liberty back.

Thus, KataGo's Bad-Shape Move reduces Black's territory in the left centre by one point (in the Capture Variation), without effectively losing one tempo in the Main Semeai, as usual with this type of territory-destroying moves.

For further details, please refer to section "KataGo's Bad-Shape Move in the Left Centre" ( 2039)

:
It is best for Black to give atari at White's two stones in the lower left.

Immediately occupying White's liberty at is possible, in principle, but will lose points in the Semeai Variation unnecessarily.

For further details, please refer to section "KataGo's Bad-Shape Move in the Left Centre" ( 2039a) or ...

... to the history of our investigations ...
548kj

Playing tenuki to , in order to capture White's single stone in the right centre, was an idea of Joachim, resulting in a novel skirmish in the left centre of the board.
However, as it turned out in the very end, Black could not benefit from this deviation. Quite the contrary, White would win the Semeai Variation, too.

For further details, please refer to section "KataGo's Bad-Shape Move in the Left Centre" ( 2039b) or ...

... to our very detailed historical analysis under the framework condition "No Early Kikashi" ...
513a

Please note that it would result a change in the order of moves with the sequence shown below, if Black played KataGo's Solid Connection in the left centre first.

:
And yet another "early" kikashi, typical for KataGo.

:
White connects in the lower left, saving her two stones that were in atari.

Please note that this connection is possible, only because the endgame in the upper left and lower left corners has already taken place.
This move loses two tempi in the Main Semeai, so otherwise Black would be able to e.g. defend his territory in the (then still open, and unsettled) upper left corner.

Please also note that this connection not only secures White quite a lot of points (locally), but also unlocks the cutting-point in the left centre.

:
Black must defuse this cutting point, and does so with KataGo's Solid Connection in the left centre: Please note that this move loses one tempo in the Main Semeai.

Black must play very cautiously and carefully here, because his weakness in the left centre is far more massive than it appears at first glance.
This fact was already discussed a few moves earlier.

Please also refer to the history of our investitation for some variations after Joachim's Tenuki with at , which will worsen Black's score in the Semeai Variation ...
649af

:
White is forced to prevent her single stone in the right centre from becoming captured by Black, due to the loss of two Main Semeai Liberties by her connection with .

:
Due to White's earlier loss of Main Semeai Liberties, Black is able to push at the top, in sente, so destroying one point of White's territory at the top.

He must not do so before White's connection with in the lower left. Otherwise, White will answer by occupying a liberty of Black's large group in the upper right, e.g. with , and Black will fall prey to the Punishment Semeai thereafter.

:
White is forced to block immediately.

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Black captures White's single stone at the upper edge, so losing a tempo in the Main Semeai. He has still one surplus Main Semeai Liberty left.

Please note that this move is only possible because White has previously connected her two stones in the lower left with . KataGo's Immediate Crosscut 's true value (three points) is reduced by one point by this combinatorial effect.

:
White prevents Black from taking profit outside the Main Semeai Area, in sente. This will benefit her in the Semeai Variation.

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White gives atari at the upper edge.

KataGo likes to continue with , instead.
However, this move allows Black to give atari at , gaining profit outside the Main Semeai Area after , . Black would benefit by two points in the Semeai Variation (but which is irrelevant for KataGo).

:
Black will connect.

He destroyed two points of White's territory at the upper edge at the cost of only one tempo in the Main Semeai.
Black's territorial gains at the top partially compensate for his large loss in the lower left, caused by White's connection .

:
The Main Semeai continues.

Please note that it does not make any sense to reduce Black's territory at the left (for the Capture Variation), starting with moves at , or , instead, which KataGo's 2019 version still couldn't let go of.
Black has more than enough opportunities at the right side of the board for compensation, so this kind of mutual reduction of opponent's territory (for the Capture Variation) would simply be a waste of time.

:
Sooner or later, White will capture the nakade for the first time.

:
Black's peep at the left edge starts the creation of a five-stone nakade.

:
White connects immediately.

Alternatively, she could answer with a move at , changing the order of moves.

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KataGo likes to play this atari first.

:
The final mutual occupation of opponent's liberties in the Main Semeai starts with this move.

In this very late phase of the game, Fujisawa Hideyuki made several technical mistakes regarding the correct order of moves (which were largely adjusted by Jérôme Hubert). He violated a fundamental principle of the endgame by occupying worthless points before valuable ones, but this had no effect in his own classical solution.

For further details, please refer to section "Jérôme Hubert's Correction of the Mutual Occupation of Opponent's Liberties" ( 2041).

You will be able to see from studying this section that even professionals can err in uncomplicated positions.

: (A 2022e)
Black destroys one point of White's territory in the right half of the board, in exchange for the loss of one tempo in the Main Semeai.

Thereafter, he is back at par with the Punishment Semeai Liberty Level.

Black must not lose another tempo in the Main Semeai, e.g. by connecting his single stone in the lower right with a move at , instead.
He would be punished severly for this mistake.

:
White captures the nakade for the second time.

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Black's oki starts the creation of a four-stone nakade.

:
We follow the classical line of play here with the filling of the nakade, resulting in a pyramid shape.

However, as Ōhashi Hirofumi 7p told us, continuing with a move at would be the technically correct move (despite not affecting the outcome of this game), resulting in a square shape of the nakade.

For further details, please refer to section "Ohashi Hirofumi's Order of Moves in the Nakade" ( 2040).

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Black completes the four-stone nakade, also giving atari at White's left-hand group.

: (A 2022g)
We have reached White's decision point.
Black's large group at the right has seven liberties left.

KataGo likes to capture the hanezeki's tail immediately, so entering the Capture Variation.

Choosing the Semeai Variation (being worse for White, as Black would end four points ahead), instead, would require the capture of the nakade with .

Playing the exchange of , before capturing the hanezeki's tail – as in the classical solution – would not affect the outcome of the Capture Variation. Both sides would have added one stone to the nakade area.

:
Black recaptures.

: (A 2022h)
White plays Joachim's Rediscovered Oki.

In his solution, Fujisawa Hideyuki continued with further occupying Black's liberties (in a slightly different scenario in the right centre), but which was a mistake.

For further details, please refer to section "Joachim's Rediscovered Oki in the Hanezeki" ( 2042).

:
Black is forced to approach White's corner group in the hanezeki.

Black is unable to connect at , instead. would take Black's group an all-decisive liberty.

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White's cut is sente, also allowing her to capture Black's single stone to the left.

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Black's oki is mandatory.

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Capturing Black's single stone is sente again.

; :
Typical for an AI programme, KataGo likes to insert some kikashi.

:
Finally, Black takes White's group in the temporary seki off the board.

Capture Variation:

Compared to our 2017 solution, ...
– White destroyed two points of Black's territory in the upper right corner.
– Black captured one White stone at the upper edge, so gaining one point.
– White gained one additional point of territory at the upper edge, but lost one point of territory at the top, so the net effect is zero.
– White destroyed one point of Black's territory in the left centre.
– White captured one Black stone in the lower left, so gaining one point.
– White destroyed five points of Black's territory in the lower left.
– Black destroyed one point of White's territory in the right centre.

In total, White gained seven points.

Black + 5 => White + 2